[1]} show that Assumption REF  is satisfied if the measures \(\pi ^{(\ell )}\)  satisfy a Stein log-Sobolev inequality. [2]} also show that Assumption REF  is satisfied for a specific choice of the kernel \(K\) . We also note that the exponential convergence rate for the KL divergence appears in the theory for the convergence of Markov processes when the target measure satisfies a log-Sobolev inequality [3]}; however, SVGD approximates the gradient in an RKHS and thus [3]} is not directly applicable.
